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TitleAn alternative approach to comprehensive Gröbner bases
Author(s) Yosuke Sato, Akira Suzuki
TypeArticle in Journal
AbstractWe give an alternative definition of comprehensive Gröbner bases in terms of Gröbner bases in polynomial rings over commutative Von Neumann regular rings. Our comprehensive Gröbner bases are defined as Gröbner bases in polynomial rings over certain commutative Von Neumann regular rings, hence they have two important properties which do not hold in standard comprehensive Gröbner bases. One is that they have canonical forms in a natural way. Another one is that we can define monomial reductions which are compatible with any instantiation. Our comprehensive Gröbner bases are wider than Weispfenning’s original comprehensive Gröbner bases. That is there exists a polynomial ideal generated by our comprehensive Gröbner basis which cannot be generated by any of Weispfenning’s original comprehensive Gröbner bases.
KeywordsGröbner basis
Length19
ISSN0747-7171
File
URL dx.doi.org/10.1016/S0747-7171(03)00098-1
LanguageEnglish
JournalJournal of Symbolic Computation
SeriesISSAC 2002
Volume36
Number3-4
Pages649-667
PublisherAcademic Press, Inc.
AddressDuluth, MN, USA
Year2003
Edition0
Translation No
Refereed No
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